Experiencing Manipulative Material for the Teaching and Learning of Mathematics

This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.

Mathematics teaching life histories in the study of teachers' perceptions of change

The aim of this paper is to discuss teachers' perceptions of change in their thought and/or practice over time and their perceptions of what kind of experiences or challenges might have influenced those changes. Two mathematics teaching life histories of Brazilian teachers are examined, considering a context of curriculum development in the state of São Paulo, Brazil. Reflection on teachers' thought and practice and interest in their own development, including interest in their own learning of mathematics, seemed to be the most important internal aspects influencing change and development. Close support seemed to be the most important external aspect. The retrospective analysis put a good face on personal change and development. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

Structuralism and the Applicability of Mathematics

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

Dynamics of change of mathematics education in Brazil and a scenario of current research

Mathematics education in Brazil, if we consider what one may call the scientific phase, is about 30 years old. The papers for this special issue focus mainly on this period. During these years, many trends have emerged in mathematics education to address the complex problems facing Brazilian society. However, most Brazilian mathematics educators feel that the separation of research into trends is a theoretical idealization that does not respond to the dynamics of the problems we face. We raise the conjecture that the complexity of Brazilian society, where pockets of wealth coexist with the most shocking poverty, has contributed to the adoption and generation of different strands in mathematics education, crossing the boundaries between trends. At a more micro level, we also raise the conjecture that Brazilian trends in research are interwoven because of the way that Brazilian mathematics educators have experienced the process of globalization over these 30 years. This tapestry of trends is a predominant characteristic of mathematics education in Brazil. © FIZ Karlsruhe 2009.

The USAID and the teaching of mathematics in Rio Grande do Norte

In the 1960s occurred great changes in the general education and, specially in the mathematical teaching, throughout Brazil. Besides the Law Diretrizes e Bases for Education (law 4024/1961), such changes also was occurred by opposite educational movements. In one side, those ones that valorized the popular education and culture and, for the other side, the international agreements between universities and government organs, like SUDENE and MEC, with United States Agency for International Development (USAID). These agreements purposed the cultural alignment. In this article we will expose some of these agreements and their interference in two courses for teachers' education. These teachers taught mathematics for the elementary school, in Rio Grande do Norte.

Trends in Brazilian academic production in the History of Mathematics Education: directions from EBRAPEM

The number of papers on History of Mathematics Education presented at EBRAPEM (Brazilian Meeting of Graduate Students in Mathematics Education) has increased significantly between 2003 and 2008. This article presents a study with the aim of identifying themes, periods in focus, and sources and theoretical and methodological references used by the authors of the papers on History of Mathematics Education published in the proceedings of VII, VIII, IX, X, XI and XII EBRAPEM. The study indicates that the approach of ongoing research in History of Mathematics Education in Brazil has been similar to the approach of research in History of Education in general. However, the institutional separation between these two areas of investigation is noted as a factor rendering communication between both groups of researchers difficult.

História na Educação Matemática – um estudo sobre trabalhos publicados no Brasil nos últimos cinco anos

In this paper we report a study on research in the field of History in Mathematics Education conducted in Brazil in the last five years. We evaluate studies that are theoretical or report experiences on the support found in history that can contribute to the situations of teaching and learning of mathematics, based on the Proceedings of Seminarios Nacionais de Historia da Matematica and Encontros Luso-Brasileiros de Historia da Matematica. Examining the interests, directions and focus of research in the field, we found that the vast majority of studies address specific issues of History of Mathematics, and the number of studies on History in Mathematics Education is still very low. We note that, in the last five years, the arguments in favor of the teaching potential of the History of Mathematics, which is very present in the speech of teachers and managers of public education, has not yet been materialized in experiments or investigations to promote this link effectively.

A aprendizagem matemática em uma posição de fronteira: Foregrounds e intencionalidade de estudantes de uma favela brasileira

In a large metropolis, students from different neighbourhoods can experience very different life opportunities. This can influence their attitude towards schooling and learning, including the learning of mathematics. We interviewed a group of six students from a favela in a large city in the interior of the state of São Paulo in Brazil. We invited the students to look into their future and explore whether or not there could be learning motives that linked mathematics in school to possible out-of-school practices, either in terms of possible future jobs or further studies. We identified some themes in the students' descriptions of their experiences. The first theme is discrimination. The students feel discriminated against due to the fact that they come from a poor neighbourhood. They fear being trapped in some stereotypes. The second theme is escape. There is a strong motivation to begin a new life away from the favela. A third theme concerns the obscurity of mathematics. It seems clear to everybody that education is relevant to ensure a change in life. However, the mathematics lessons do not provide any clues regarding how mathematics might function is this respect. The fourth theme is uncertainty with respect to the future. The students could easily formulate almost unattainable aspirations, while reality might impose some very heavy limitations. In this article we introduce a theoretical framework for discussing the relation between favela students' life conditions in relation to their educational experiences and opportunities. Students' intentions for learning are related to their foregrounds, that is, how they perceive their future possibilities, as made evident to them by their social environment. Students in a favela could experience what we call a borderland position, a relational space where individuals meet their social environment and come to terms with the multiple choices that cultural and economic diversity make available to them.

A metodologia de resolução de problemas: concepções e práticas pedagógicas de professores de matemática do ensino fundamental

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